| Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1071 | Structured version Visualization version GIF version | ||
| Description: Technical lemma for bnj69 35024. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| bnj1071.7 | ⊢ 𝐷 = (ω ∖ {∅}) |
| Ref | Expression |
|---|---|
| bnj1071 | ⊢ (𝑛 ∈ 𝐷 → E Fr 𝑛) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bnj1071.7 | . . 3 ⊢ 𝐷 = (ω ∖ {∅}) | |
| 2 | 1 | bnj923 34782 | . 2 ⊢ (𝑛 ∈ 𝐷 → 𝑛 ∈ ω) |
| 3 | nnord 7895 | . 2 ⊢ (𝑛 ∈ ω → Ord 𝑛) | |
| 4 | ordfr 6399 | . 2 ⊢ (Ord 𝑛 → E Fr 𝑛) | |
| 5 | 2, 3, 4 | 3syl 18 | 1 ⊢ (𝑛 ∈ 𝐷 → E Fr 𝑛) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 = wceq 1540 ∈ wcel 2108 ∖ cdif 3948 ∅c0 4333 {csn 4626 E cep 5583 Fr wfr 5634 Ord word 6383 ωcom 7887 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-ral 3062 df-rab 3437 df-v 3482 df-dif 3954 df-ss 3968 df-uni 4908 df-tr 5260 df-po 5592 df-so 5593 df-fr 5637 df-we 5639 df-ord 6387 df-on 6388 df-om 7888 |
| This theorem is referenced by: bnj1030 35001 bnj1133 35003 |
| Copyright terms: Public domain | W3C validator |